Non-separable Dynamic Nearest-Neighbor Gaussian Process Models for Large spatio-temporal Data With an Application to Particulate Matter Analysis

摘要

Particulate matter (PM) is a class of malicious environmental pollutantsknown to be detrimental to human health. Regulatory efforts aimed at curbing PMlevels in different countries often require high resolution space-time mapsthat can identify red-flag regions exceeding statutory concentration limits.Continuous spatio-temporal Gaussian Process (GP) models can deliver mapsdepicting predicted PM levels and quantify predictive uncertainty. However, GPbased approaches are usually thwarted by computational challenges posed bylarge datasets. We construct a novel class of scalable Dynamic Nearest NeighborGaussian Process (DNNGP) models that can provide a sparse approximation to anyspatio-temporal GP (e.g., with non-separable covariance structures). The DNNGPwe develop here can be used as a sparsity-inducing prior for spatio-temporalrandom effects in any Bayesian hierarchical model to deliver full posteriorinference. Storage and memory requirements for a DNNGP model are linear in thesize of the dataset thereby delivering massive scalability without sacrificinginferential richness. Extensive numerical studies reveal that the DNNGPprovides substantially superior approximations to the underlying process thanlow rank approximations. Finally, we use the DNNGP to analyze a massive airquality dataset to substantially improve predictions of PM levels across Europein conjunction with the LOTOS-EUROS chemistry transport models (CTMs).